STABILITY OF HIGH DIMENSIONAL NONLINEAR SYSTEMS USING KRASOVSKIIS THEOREM

Liapunov's direct method is used to establish a finite region of asymptotic stability for nonlinear systems with an arbitrary number of state variables. The procedure is a geometric one in multidimensional space which uses the Fletcher‐Powell minimization technique to find the maximum time derivative of the Liapunov function on the closed Liapunov hypersurface. Three detailed examples are presented, the first being the classical 2‐variable CSTR with heat transfer and the third being a 32‐variable 16‐stage model of an adiabatic tubular reactor with axial diffusion. Copyright © 1969 American Institute of Chemical Engineers